Extant species diverge from their common ancestors. Evolutionary studies rely on statistical models that can estimate their time of divergence reliably based on the patterns of conservation recorded in, amongst others, their amino acid sequences and their threedimensional structures, that are subject to the evolutionary pressure of selection. Sound statistical models have been proposed for estimating the divergence of amino acid sequences over their discrete amino acid states. However, the continuous space of structures have resisted rigorous statistical treatments, and instead rely on simplistic measures involving root-mean-squared-deviation (RMSD) of structural superpositions as proxies for their divergence estimates. The work presented here overcomes this gap and proposes a statistical model inferred using the Bayesian and information-theoretic framework of Minimum Message Length. Using a large collection of 3D structure alignments, we infer a time-parameterized stochastic matrix (accounting for changes in shape of related residues) and associated Dirichlet models (accounting for insertions and deletions during the evolution of protein domains). They are used in concert to estimate the Markov time of divergence of tertiary structures in terms of the patterns of conservation of their resultant secondary structural states. Further, by analysing one million pairs of homologous structures, we are able to correlate between the Markov time of divergence of structures and sequences, something which was only possible using proxies (often in terms of variation of RMSD with sequence identity) in previous work.